Factor completely. $108-3x^2=$
Explanation: First, we take a common factor of $3$. $108-3x^2=3(36-x^2)$ Now, let's factor $36-x^2$. Both $36$ and $x^2$ are perfect squares, since $36=({6})^2$ and $x^2=({x})^2$. $36-x^2 = ({6})^2-({x})^2$ So we can use the difference of squares pattern to factor. ${a}^2 - {b}^2 =({a}+{b})({a}-{b})$ In this case, ${a}={6}$ and ${b}={x}$ : $({6})^2 - ({x})^2 =({6}+{x})({6}-{x})$ $\begin{aligned} 108-3x^2&=3(36-x^2) \\\\ &=3(6+x)(6-x) \end{aligned}$ In conclusion, the complete factorization is $3(6+x)(6-x)$ Remember that you can always check your factorization by expanding it.